Fission–fusion dynamics in the social networks of a North American pitviper

Abstract Many animal species exist in fission–fusion societies, where the size and composition of conspecific groups change spatially and temporally. To help investigate such phenomena, social network analysis (SNA) has emerged as a powerful conceptual and analytical framework for assessing patterns of interconnectedness and quantifying group‐level interactions. We leveraged behavioral observations via radiotelemetry and genotypic data from a long‐term (>10 years) study on the pitviper Crotalus atrox (western diamondback rattlesnake) and used SNA to quantify the first robust demonstration of social network structures for any free‐living snake. Group‐level interactions among adults in this population resulted in structurally modular networks (i.e., distinct clusters of interacting individuals) for fidelis use of communal winter dens (denning network), mating behaviors (pairing network), and offspring production (parentage network). Although the structure of each network was similar, the size and composition of groups varied among them. Specifically, adults associated with moderately sized social groups at winter dens but often engaged in reproductive behaviors—both at and away from dens—with different and fewer partners. Additionally, modules formed by individuals in the pairing network were frequently different from those in the parentage network, likely due to multiple mating, long‐term sperm storage by females, and resultant multiple paternity. Further evidence for fission–fusion dynamics exhibited by this population—interactions were rare when snakes were dispersing to and traversing their spring–summer home ranges (to which individuals show high fidelity), despite ample opportunities to associate with numerous conspecifics that had highly overlapping ranges. Taken together, we show that long‐term datasets incorporating SNA with spatial and genetic information provide robust and unique insights to understanding the social structure of cryptic taxa that are understudied.

Accordingly, social interactions are not only proximate events but also include those occurring at greater distances among individuals.
Historically, social interactions have been analyzed as dyadic interactions, quantified in myriad ways (Allison & Liker, 1982;Bakeman, 1997). The advent of modern network ecology has provided the requisite tools for more nuanced analyses via network theory (Croft et al., 2008;Krause et al., 2015). Although originally developed for studies of human behavior and physics (Croft et al., 2008;Pinter-Wollman et al., 2014), the conceptual and analytical framework has advanced our understanding of social networks in wild animals (Croft et al., 2008(Croft et al., , 2016Farine, 2017;Farine & Whitehead, 2015;Fortin et al., 2021;Krause et al., 2015;Webber & Vander, 2019). These networks are composed of nodes denoting individuals, groups, or other entities, and edges representing interactions (e.g., behavior) between or among nodes (Appendix A). Importantly, because social network analysis (SNA) provides a conceptual and analytical framework to explore patterns of interconnections among biological entities, it allows researchers to identify emergent group-level interaction patterns and quantify individuals' contributions to network connectedness. SNA can therefore reveal otherwise unobservable ecological patterns and the processes underlying them (Croft et al., 2008(Croft et al., , 2016Krause et al., 2015). Furthermore, by using null models, robust statistical testing can be achieved to assess whether such emergent group-level patterns differ from random association among individuals (Farine, 2017;Fortin et al., 2021;Krause et al., 2015).
Social network analysis has elucidated many insights on the social structure of animals, from insects and fishes to primates and cetaceans (Croft et al., 2008(Croft et al., , 2016Krause et al., 2015;Pinter-Wollman et al., 2014). Yet, despite such advances, there are important gaps, particularly in several specious lineages of vertebrates historically considered to not be highly social (Doody et al., 2021;Schuett, Clark, et al., 2016;. Among these lineages, reptiles in general (but see Godfrey, 2015;Godfrey et al., 2014) and snakes specifically have received particularly short shrift, with scant studies exploring social behavior under the network perspective (Doody et al., 2021). To our knowledge, of the ~4000 extant species, only one snake (Crotalus cerberus) has been studied in the wild with these tools (Schuett, Clark, et al., 2016). Most terrestrial snakes have cryptic lifestyles, and structure of their social networks is largely unknown (Doody et al., 2021;).
Yet, some species-such as large vipers, boids, and pythonids-are excellent candidates for models of SNA. For example, in many moderate-to large-sized rattlesnakes (e.g., Crotalus atrox, C. cerberus, C. oreganus, C. stephensi, and C. viridis), a variety of factors including large population size and communal winter denning render them desirable subjects to study in nature. Based on prior field research (Amarello, 2012;Clark et al., 2014;Doody et al., 2021;Schuett, Clark, et al., 2016;, it appears most snakes likely form distinct clusters of individuals interacting (i.e., modular networks) which should be defined to some extent by relatedness, but these predictions have yet to be quantitatively tested (Clark et al., 2014;Doody et al., 2021;.
Nonetheless, behavioral evidence strongly suggests the existence of fission-fusion dynamics (spatial and temporal changes in the size and composition of conspecific groups) in the social networks of many temperate rattlesnakes (Klauber, 1956;Schuett, Clark, et al., 2016;. Here, we leveraged long-term datasets for a population of a large-bodied North American pitviper, the western diamondback rattlesnake (Crotalus atrox), to test hypotheses of social network structure and fission-fusion dynamics (Aureli et al., 2008;Schuett, Clark, et al., 2016;. We asked three main questions: First, do group-level patterns emerge from distinct social interactions? Second, do individuals' traits influence their connectivity within social networks? Lastly, does genetic relatedness undergird social interactions in this system? We investigated three bipartite interactions (denning, sexual pairing, and parentage) and the drivers of individuals' centrality (Appendix A). Specifically, we tested (a) whether these three bipartite networks presented nonrandom modular or nested structure (Appendix A); (b) which attributes (body length, sex, and home range size) are associated with individuals' centrality in these three networks, and (c) whether interactions occurrence and or frequencies in the three social networks and home range overlap are significantly correlated with genetic relatedness among individuals (e.g., kin-based).

| Study system
A single population of western diamondback rattlesnakes in the Suizo Mountains (Pinal County, AZ, USA) was studied for 15 consecutive years from March 1, 2001, to December 31, 2015(Clark et al., 2014Levine et al., 2020;Schuett, Clark, et al., 2016;. The research site is 40 km SSE of the city of Florence, 8 km W of State Route 79. This region is designated as Sonoran Desert, Arizona Upland Desert-Scrub subdivision (Clark et al., 2014).
Data accumulated for this C. atrox population has contributed substantially to our understanding of the species' behavior, reproductive ecology, and life history in Arizona (Repp, 1998;Schuett, Clark, et al., 2016;. Key events of the annual cycle are summarized in Figure 1, but the typical phenology of this population is described for further clarity. Egress from communal dens is centered in late March to early April (Clark et al., 2014;Repp, 1998;Schuett, Clark, et al., 2016;.
In most cases, egress lingers-from days to several weeks-and occurs in several phases, including basking at the den entrance (often in groups), making short-range movements, and returning to the den. The spring mating period (second mating season) occurs before migration movements to their spring home range areas. Courtship and coitus may occur at the den itself or in the general area. Male combat for priority-of-access to females also may occur but is rarely observed (Schuett, Clark, et al., 2016;.
Migration movements in March and April bring individuals to their spring and summer home ranges. Furthest straight-line distances traveled from communal dens to home ranges are from several dozen meters to over 2 km (Clark et al., 2014;Schuett, Clark, et al., 2016;; mating (first mating season), skin shedding, and hunting prey are the primary behavioral activities during this time (Clark et al., 2014;Schuett, Clark, et al., 2016;, and except for the two distinct mating seasons, there is generally little contact observed among adults, especially males. In fall (late October through November) adult individuals initiate migration to return to their respective communal dens to re-establish longterm social groups (networks) lasting for up to 5 months (November through March). The most common social activity at the communal dens which can be observed in all winter months is termed "sun basking" and occurs at the entrance or alongside the den itself (Repp, 1998;Schuett, Clark, et al., 2016;.
Females will sometimes alternate year to year from communal dens to overwintering singly in shelters such as rodent middens and small mammal burrows (Schuett, Clark, et al., 2016;. Males show near absolute fidelity to communal dens but rarely overwinter privately in granitic rubble.
snakes (Dormann et al., 2009). After processing, all subjects were released at their exact capture site.

| Radio-tracking
Focal animals were radio-tracked minimally 2-4 times per month during winter. Tracking was increased substantially-sometimes daily or twice daily-from early August through mid-September, the period of birthing. During spring and fall, snakes were tracked weekly on average. For each animal location, UTM coordinates were recorded along with behavioral data (particularly if associating with conspecifics), body and environment temperatures, feeding and ecdysis status, plant associations, subject location (above or below the ground surface), visible or not visible, and health status (Amarello et al., 2010;Levine et al., 2020Levine et al., , 2021Repp, 1998;Schuett, Clark, et al., 2016;.

| Spatial analyses
We estimated home range sizes by creating 100% minimum convex polygons (MCPs) around the outermost radiotelemetry locations for each snake in ArcGIS Pro 2.6.1. To produce a single value for the degree of overlap for each possible pair combination of telemetered snakes, we calculated the average overlap for the two individuals in each pair as (AB/A + AB/B)/2, where A is the home range size of individual A, B is the home range size of individual B, and AB is the area shared by both A and B. Using this method, we generated a pairwise matrix of average home range overlap values (Clark et al., 2014).

| Genotype data
All social network analyses performed in this study that incorporated DNA-based information was accomplished using previously published data (Clark et al., 2014;Schuett, Clark, et al., 2016;. See these studies for all procedures used in DNA sampling, extraction, genotyping, and parentage and relatedness analysis.

| Social network analysis
We built an interaction matrix for each social interaction considered (denning, pairing, and parentage; Appendix A). The denning network was a matrix of all male and female study subjects as rows and columns containing 1s and 0s indicating whether a given pair of all possible pair combinations of snakes from either sex were observed sharing the same den ( Figure 2a) or not, respectively. The pairing network was a matrix with females represented in columns and males represented in rows, containing a series of 1s and 0s indicating whether each possible male-female pair combination was observed engaging in any behavior associated with mating or not, respectively; examples of pairing behavior included male-female pairs in copulation ( Figure 2b) or whose bodies were in contact (e.g., males lying on females) or proximity during either mating season.
The parentage network was a matrix with females represented in columns and males represented in rows, containing a series of 1s and 0s indicating whether each possible male-female pair combination produced offspring or not, respectively; relatedness among individuals was determined from tissues such as blood or shed skins from adults and neonates (Figure 2c,d).
We tested whether the distribution of interactions among individuals presented modular or nested structure. Modularity was calculated using the metric Q and the algorithm DIRTLPAwb+ which searches for the optimum division of the observed interaction matrix into modules (Beckett, 2016). Q ranges from 0 to 1 (perfectly modular). Nestedness was estimated using the NODF metric which calculates the non-overlap and decreasing fill of the interaction matrix (Almeida-Neto et al., 2008) or WNODF, which is the equivalent for quantitative matrices, that is, interaction F I G U R E 2 Examples of interactions used to quantify social network structures for western diamondback rattlesnakes (Crotalus atrox) inhabiting the Suizo Mountains in Arizona, USA: (a) Adults occupying a communal den, (b) male and female copulating, (c) mother with neonates and (d) shed skins used to genotype individuals. Photographs (a, c, and d) taken by Roger Repp, and B taken by Brendan O'Connor.
frequencies measured (Almeida-Neto & Ulrich, 2011). Both NODF and WNODF ranges from 0 (no nestedness) to 100 (perfectly nested). We used a null model to test the significance of the observed Q and NODF/WNODF by comparing the metric calculated for the observed interaction matrix with the metric calculated from random matrices generated with a null model. Specifically, we used the vaznull null model which reshuffles interaction within a matrix while keeping the number of individuals and connectance (i.e., the proportion of realized links in relation to the total possible) the same as the observed matrix. We considered the metric significant when the observed value was higher than the 95% confidence interval produced by the null model. To quantify individuals' connectivity within each network, we calculated their closeness centrality (CC; Appendix A). This metric quantifies the proximity of a node (individual, in this case) to all other nodes in the network (Freeman, 1979;Martín González et al., 2010) indicating nodes that are more connected and, therefore, are highly influential in the network. All analyses were conducted using the bipartite package (Dormann et al., 2009) in R version 4.0.5 (R Core Team, 2022).
To investigate whether individual-specific variables were associated with individual's centrality in a network, we used generalized linear mixed models (GLMMs) where CC was the response variable and sex, snout-vent length (SVL), body mass, and MCP were predictors. Since we detected high correlation between SVL and body mass (Pearson's r = .87), we excluded body mass from our models, given lower variation in SVL measurements among individuals (Fortin et al., 2021;Pinter-Wollman et al., 2014).

| Subjects
From 2001 to 2015, we sampled 299 individuals: 191 were adult individuals and 108 neonates from 30 different litters produced by 18 different females (Clark et al., 2014). There were 15 additional unmarked males identified via genotyping who sired offspring that were considered in the parentage network (Clark et al., 2014). The denning network was composed of 23 adult individuals (all but two in the focal group with radio-transmitters), summing up 27 combinations of individuals sharing a den. Few snakes were given IDs during processing at communal shelters and used for aspects of this study (such as relation of relatedness to den choice), but were not radiotracked (e.g., CA-99; Table 1

| Landscape use
Despite considerable individual variation, males had larger and less variable average estimated spring-summer home range sizes (13.36 ha ± 9.26 SD) than females (5.08 ha ± 4.44 SD). MCPs for individuals tracked over multiple years were remarkably consistent in size and shape (see Figure A1 for an example). We observed substantial overlap of many snakes' home ranges, especially for individuals

| Home range overlap and relatedness
Mantel tests comparing home range (MCP) overlap with relatedness revealed there was no correlation between the degree of pairwise home range overlap and relatedness (r = .004, p > .05).

| Communal den occupants
With few exceptions, all telemetered individuals that used communal dens exhibited absolute fidelity to these sites over the 10-year period where snakes were consistently radio-tracked (Table 1). For example, CA-1, the longest-tracked snake in this study, showed fidelity to den AD1 for the seven winters it was tracked. Conversely, females CA-2 and CA-77 used a communal shelter for only one winter and were otherwise observed overwintering privately.
Similarly, male CA-55 used a communal shelter twice in three winters ( Table 1).

| Network structure analysis
We detected modularity in all three social networks (denning, pairing, and parentage), but no network was nested. Specifically, the denning network was modular (Q = 0.73; 95% CI Q null = 0.63-0.72) presenting six modules, including one to six individuals sharing a den, while there was no evidence of nestedness (NODF = 12.80; NODF null = 7.47-15.57). The pairing network was modular (Q = 0.77; 95% CI Q null = 0.64-0.72) presenting 11 modules including one to four males and one to four females, and there was no evidence of nestedness (NODF = 6.10; NODF null = 5.13-9.23). The parentage network was modular (Q = 0.74; 95% CI Q null = 0.61-0.73; analysis based on quantitative matrix) presenting 10 modules including one to five males and one to three females and there was no evidence of nestedness (WNODF = 8.21; 95% CI WNODF null = 6.70-12.42). In all three networks, few interactions were recorded outside the modules (n = 0 in the denning network, n = 5 in the pairing network and n = 12 in the parentage network; Figure 4).

F I G U R E 3
Spatial data on our focal group (22 males, 28 females) of adult Crotalus atrox. (a) Annual home ranges (minimum convex polygons; MCP) of males (blue) and females (orange) that were observed overwintering in communal dens (AD = den ID). (b) Sites where males overwintered in isolation (pink diamonds) or communal dens in relation to their annual home range; (c) Home ranges of males and females that were observed engaging in reproductive behaviors. (d) Sites where females gave birth (blue triangles) and overwintered privately (pink circles) or in communal dens (white squares) in relation to their home range. TA B L E 1 Data on the use of eight communal dens by a subset (11 adult females, 20 adult males) of the focal group (subjects fitted with radio-transmitters) of adult Crotalus atrox studied in the Suizo Mountains, Arizona (2001Arizona ( -2010 Note: The focal group (N = 50) consisted of 22 adult males and 28 adult females. Numbers denote abbreviated IDs of the radio-tracked subjects (CA-1 is 1, CA-5 is 5, and so on) and color denotes sex (orange = females, blue = males). AD = den ID. See text, Appendix A and Appendix S1 for additional information.
Generalized linear mixed models indicated that individuals' CC in the denning, pairing, and parentage networks were not associated with individuals' morphology (SVL) and home range (MCP) (Tables A1-A6). Sex was a significant predictor only in the parentage network, with females having slightly higher CC than males (β = −.016, 95% CI: −0.034, −0.002; Table A6).
Overall CC was low, varying from 0 to 0.14 in the denning network, 0 to 0.11 in the pairing network, and 0 to 0.08 in the parentage network (Table A7). Because many individuals were not observed interacting, it was common to have individuals whose CC = 0 (Table A7).

| Overview
In our long-term study of the behavioral ecology of adult western diamondback rattlesnakes, all three bipartite networks tested were modular and lacked nestedness (Croft et al., 2008;Krause et al., 2015;Newman, 2006 (Amarello, 2012;Schuett, Clark, et al., 2016). Adult male and female C. cerberus exhibited non-random association and formed multiple subgroups at communal dens and shelters, yet few dyads had strong associations. More studies are needed to understand the structure of social networks of snakes in general, but we suspect most would not show nested structure. In sharp contrast, the social networks (particularly related to mating) of other terrestrial vertebrates, including African lions (Mbizah et al., 2020), equids and other ungulates (Rubenstein et al., 2015), great apes and other primates (Macdonald & Voelkl, 2015), and several squamates (Bull et al., 2012;Godfrey, 2015;O'Connor & Shine, 2003), are characterized by one or several males that dominate a group of females and likely are the only ones to interact with most or all partners in a group (Krause et al., 2015).
The low CC values obtained reinforces the lack of nestedness and existence of modularity, indicating that each focal subject interacted only with a few other individuals in the three social networks examined. Furthermore, centrality was not significantly predicted by body size, home range, sex, or genetic relatedness. In this social environment, individuals with large bodies or large home ranges do not den, pair with more sexual partners, or produce more offspring than smaller and/or spatially restricted individuals (Dormann et al., 2009;O'Connor & Shine, 2003). Nonetheless, we found females had greater centrality than males in the parentage networkmeaning that they produce more offspring with a greater number of partners than males-yet this effect, though statistically significant, is not robust (Levine et al., 2021).
Genetic relatedness of our focal group was not correlated with denning, pairing, or parentage. Spatial analyses revealed that home Inner boxes indicate subsets of individuals interacting preferentially with each other (i.e., modules). In (a), individuals of both sexes can be at the x-and y-axes since multiple males and females may share a communal den. In (c) color intensity indicates the number of offspring sired. In (c), UM indicates "unidentified male" (sampled but not radio-tracked; see text). Nine unidentified males were genotyped in the analysis: UM 1-4, 7-9, and 10, 13. See Dormann et al. (2009). Snakes with IDs that end in "m" are males and "f" are females.
range overlap also was not significantly correlated with relatedness; thus, social structure between pairs of individuals during the active season was not based on kin associations (Clark et al., 2014;Schuett, Clark, et al., 2016; Appendix S1 Group living involves close relatives in some cases (Alexander, 1974; O As we discuss later, however, when a larger sample of subjects included unmarked adults (e.g., no radio-transmitters) was analyzed, the relationship of communal denning and relatedness of C. atrox showed mixed results, with multiple communal dens containing related occupants (Schuett, Clark, et al., 2016, pp. 196-198;See Appendix S1, Tables S1-S8).

| Annual cycle of communal denning and associated behaviors
The modular and non-nested structure of the denning network emerged likely via several components of the species' behavior.
Communal denning in rattlesnakes has continued to be documented (Klauber, 1956;Schuett, Clark, et al., 2016;Sexton et al., 1992), most extensively in timber rattlesnakes (Crotalus horridus) in the northeastern United States. Adult and juvenile C. horridus typically use communal dens (termed hibernacula), exhibiting high levels of natal den philopatry. In the western United States, numerous rattlesnake species are known to use communal dens in winter, but sometimes are active year-round (Amarello et al., 2010;Brown, 2016;Graves & Duvall, 1995;Repp, 1998;Schuett, Clark, et al., 2016;Sexton et al., 1992). These species that den communally often show high fidelity to dens (reviewed in Schuett, Clark, et al., 2016). However, studies lasting >5 years on individual occupancy and behavioral activities at communal dens remain rare (Booth & Schuett, 2011;Brown, 2016;Loughran et al., 2015;Schuett, Clark, et al., 2016;. The social ecology of adult male and female C. atrox at the Suizo Mountain site represents fission-fusion dynamics, per Aureli et al. (2008), associated with annual migrations to spring-summer home range areas and fidelity to communal winter shelters (Clark et al., 2014;Repp, 1998;Schuett, Clark, et al., 2016;. In this system, adults occupy specific microhabitats throughout their respective spring-summer home ranges of the Sonoran Desert landscape. During spring and summer, mating, shedding, and hunting prey are the primary behavioral activities (Clark et al., 2014;Schuett, Clark, et al., 2016;, with generally little contact observed among adults (especially males) despite substantial overlap in home ranges. On several occasions, females were found together on the ground's surface, or inside a mammal burrow or midden, and sometimes this is associated with birthing (Schuett, Clark, et al., 2016;. However, birthing rookeries described in other rattlesnakes, which sometimes consist of a dozen or more females (Graves & Duvall, 1995), were never observed in C. atrox, nor were communal dens used as birthing sites in this study (Figure 3). Furthermore, neonates and juveniles were never observed at communal dens; thus, we presume they were isolated in rodent middens, small mammal burrows, or similar types of shelters during winter.

| Communal denning and relatedness
Based on Hamilton's foundational insights (Hamilton, 1963(Hamilton, , 1964, and others' subsequent work (Alexander, 1974;Trivers, 1972;Wilson, 1975), we have a robust understanding of the evolutionary benefits and costs of group living (Dugatkin, 1997;Wittenberger, 1981). Benefits for both kin-and non-kin-based social groups include increased vigilance to predators and enemies, protection from the environment, increased opportunities for reproduction, and the expression of social behaviors including grooming and parental duties (e.g., uniparental, biparental, and helpers).
Living in exclusive kin-based groups, such as families (Emlen, 1995) offers individuals opportunities for increasing their inclusive fitness, among other benefits (Hamilton, 1964). Under these conditions cooperative and altruistic behaviors can evolve, such as forsaking reproduction and caring for the progeny of relatives (Hamilton, 1963).
Living in groups also has costs, which can be severe, and include the spread of parasites and disease, limited numbers of mates, and competition for food and space itself (Dugatkin, 1997;Evans et al., 2015;Wittenberger, 1981).
Our bipartite analysis of the focal group of adult C. atrox showed that relatedness was not a significant component of the social structure of occupants at communal dens. Only 23 of 50 focal subjects were associated with communal dens (Figure 4a).
However, using a larger sample of individuals derived from previous analyses (Clark et al., 2014;Schuett, Clark, et al., 2016), overall genetic relatedness among dens was significantly greater than random (Appendix S1, Tables S1-S8). Although kin recognition has not been documented in C. atrox, it has been documented in other pitvipers, including rattlesnakes (Clark, 2004;Hoss et al., 2015).
Thus, we suspect that C. atrox shares this capacity for kin recognition, even if it does not appear to be a major driver of its social networks. Empirical studies could determine whether kin recognition is operating at the communal dens and expressed in social preferences (Clark et al., 2012). In the only other study of rattlesnakes where relatedness of occupants of communal dens has been measured, juveniles and pregnant females preferentially associate with kin under certain conditions, yet communal denning was not kin-based (Clark et al., 2012).

| Social groups versus aggregations
Communal denning is a type of clumped spacing behavior often defined as "aggregation" (Schuett, Clark, et al., 2016). However, with respect to C. atrox in this study, and likely other rattlesnake species, we abandon use of the term "aggregation" and alter the lexicon by defining communal denning as the formation of social groups or colonies by individual preference. We suggest that these groups form and evolve through mutual attraction of individuals (regardless of members' relatedness) for cooperative benefits to survival and reproduction (Evans et al., 2015;Hamilton, 1964;Hatchwell, 2010). These social groups we observed, whether kin-or non-kin-based, occur seasonally in a predictable manner. Remarkably, over the 15-year period of study, the focal group of adults showed near-absolute fidelity to communal den sites.
Several females, however, alternated year to year from communal dens to overwintering singly in shelters such as rodent middens and small mammal burrows (Schuett, Clark, et al., 2016;. Adult males in our population, on the other hand, never occupied these kinds of temporary structures during the cooler months (November through March). This sexually dimorphic behavior related to den use in winter has not been described, to our knowledge, for any snake species (Amarello et al., 2010;Repp, 1998;Sexton et al., 1992). Furthermore, because we never observed neonates or juveniles of C. atrox at the communal dens used by the adults; we presume that they were isolated and alone in rodent middens or small mammal burrows during winter. This also contributes to the high level of modularity observed of the denning network.

| Pairing network
Emerging research on the social environment increasingly reveals that sexual selection is dynamic, varying both temporally and spatially. Moreover, individuals frequently select for specific social environments, with direct implications on fitness (Bull et al., 2012;McGlothlin et al., 2010;Wolf et al., 1999) as social conditions (e.g., population density, opportunities for interaction, etc.) provide critical contexts for sexual selection (Oh & Badyaev, 2010;Procter et al., 2012). However, this can be buttressed by relatedness as related individuals may be less likely to harm conspecifics (Pizzari et al., 2015) or more likely to disperse to avoid harm (Faria et al., 2019), ostensibly improving individuals' inclusive fitness.
Although some interactions related to mating behavior were likely not observed because snakes were intermittently located with radiotelemetry, in our study we revealed that the pairing network is modular and largely driven by focal females interacting via reproduction-linked behaviors with multiple males, and often during fusion events at winter shelters. Perhaps more interestingly, some female C. atrox in this network occasionally leave communal dens they historically occupied, overwinter solitarily, and then return to their preferred communal dens in subsequent years. The mechanism behind this phenomenon is unclear, but it suggests that females are modulating their participation in the social environment, perhaps with considerable fitness consequences. We speculate that because pitvipers are generally capital breeders, conditions might arise in which lack of resources would render reproducing risky in the following season. Thus, by modulating their social environment, females may exert some control over reproductive output. And while we did not find a positive association between pairing and relatedness among focal (i.e., radio-telemetered) animals, positive relatedness among all individuals in communal dens was revealed in previous studies of this system (Schuett, Clark, et al., 2016;.

| Parentage network
Recent studies show that the social environment itself may influence the pattern of paternity levels in general, and multiple paternity among individuals specifically (Baden et al., 2020;Bull et al., 2012). nity. In addition, despite data that indicate communal denning (social groups) in this population show some level of relatedness (Schuett, Clark, et al., 2016;, the parentage network of our focal animals was not positively correlated with relatedness, which is indicative of some degree of either assortative mating or inbreeding avoidance. Ultimately, the social environment coupled with the species biology appears to promote elevated levels of multiple paternity but depress the degree of inbreeding among males and those females acting as nodes in the social network.

| CON CLUS IONS
Nearly three decades ago the first theoretic analysis of snake mating systems was proposed (Duvall et al., 1993) which identified, characterized, and quantified snake mating systems within formal selection theory (Arnold & Duvall, 1994). Over the years, a wealth of new information on population genetics, behavior, reproduction, sexual selection, and parental care of snakes has emerged (Booth & Schuett, 2011Greene et al., 2002;Jellen & Aldridge, 2011;Levine et al., 2021;Rivas & Burghardt, 2005;Schuett, Clark, et al., 2016;. We contend that the incorporation of social network analysis into studies documenting spatial ecology, habitat use, and genetic relatedness represents another major methodological advance that can provide novel insights and directions for future research (Schuett, Clark, et al., 2016;. Specifically, we demonstrated strong fissionfusion dynamics, particularly with respect to annual migrations to spring-summer home ranges and use of communal dens during winter by a combination of social preference and experience; relatedness (kin association) also may play a role. Although this fission-fusion behavior has not been formally reported for other snake species, we suggest it may be more common than currently recognized and urge researchers to leverage myriad existing similar datasets to further quantify social network structures for such cryptic and understudied species. Arguably, our study advances the understanding of individuals' reproductive strategies within populations and between the sexes by identifying determinants of social interaction patterns and individual fitness and lays the foundation for additional research into the social ecosystem of cryptic taxa.
Despite this substantial progress in our understanding of snake mating systems, several important issues are problematic and remain unresolved. We conclude with four intriguing examples. Our view is that social networking analyses similar to those we have employed here will be a critical method necessary for addressing all of these questions.
First, perhaps the most perplexing issue in our system is the presence of two distinct mating seasons, which is rarely present in other reptiles (Clark et al., 2014;Graham et al., 2008;Schuett, Clark, et al., 2016;. To date, there has been little theoretical research into this phenomenon. The two annual reproductive periods are temporally distinct and present decidedly different socio-ecological contexts. Furthermore, because these distinct mating periods occur prior to ovulation in late spring (Schuett, Clark, et al., 2016;; Figure 1), increased mating opportunities for both sexes provide a possible adaptive explanation for their occurrence (Arnold & Duvall, 1994;Duvall et al., 1993;Parker & Birkhead, 2013;Shuster et al., 2013 (Duvall et al., 1993), as in this system (Clark et al., 2014;Schuett, Clark, et al., 2016;? Numerous adaptive explanations have been proposed but have yet to be investigated empirically. For example, by having several partners per annum the likelihood of multiple paternity increases and thus the possibility for greater genetic and phenotypic diversity per litter (including, perhaps, diversity of social behaviors) (Clark et al., 2014;Parker & Birkhead, 2013;Shuster et al., 2013), which could result in higher overall lifetime reproductive success despite the inherent costs incurred by mating multiply (e.g., increased energetic investment, exposure to disease, and predation).

Third, information on how individual C. atrox and other snakes
first come to learn and delineate their home range and other preferred spatial locations (such as communal dens) is sparse, at best.
For instance, is a snake's home range inherited from, or part of, their mother's home range, and thus is acquired and learned via maternal social transmission (Hobaiter et al., 2014;Ilany & Akcay, 2016;Szabo et al., 2021)? We envision this process might be further facilitated by behavioral (kin-and self-recognition, individuality) and chemosensory (pheromones) social information gleaned from conspecifics Cobb et al., 2005;Ford, 1986;Mason & Parker, 2010;Muellman et al., 2018;Waters et al., 2017). As technological advances debut, particularly the miniaturization of tracking devices (Beaupre, 2016), understanding the ontogeny of home range development, social networks, and space use in snakes from birth to adulthood will be important to explore (Schuett, Clark, et al., 2016;.
Finally, we are aware of populations of C. atrox, even within several kilometers of our study site at the Suizo Mountains that do not exhibit communal denning (Schuett, Clark, et al., 2016;. To a large extent, the type of landscape (e.g., geology) appears to dictate whether communal denning is present in a population, and thus could be a critical additional data layer to incorporate into social network analyses. For example, we have noted that igneous rock formations are not used by C. atrox for communal denning (Schuett, Clark, et al., 2016;.

ACK N OWLED G M ENTS
Numerous individuals provided assistance in the field and radio-

CO N FLI C T O F I NTER E S T S TATEM ENT
The authors declare no conflicts of interest.
Mixed effects models and extensions in ecology with R. Springer.

S U PP O RTI N G I N FO R M ATI O N
Additional supporting information can be found online in the Supporting Information section at the end of this article.

A PPE N D I X A
Definitions of important terms in social network ecology that were used in the present study

Association index
Any measure of the strength of association between two species (Croft et al., 2016;Godfrey et al., 2014).

Centrality
The extent to which a given node (e.g., individual) occupies a position that is important in the structure of the network (Croft et al., 2016;Godfrey et al., 2014).

Closeness centrality
A measure of centrality that quantifies the proximity of a node (e.g., individual) to all other nodes in the network and thus indicates nodes that are more connected and highly influential in the social network (Graves & Duvall, 1995;Loughran et al., 2015).

Fission-fusion dynamics
The extent of variation in spatial cohesion and individual membership in a group over time (R Core Team, 2022).

Modularity
A measure of subsets (groups, clusters, or communities) of entities (e.g., individuals) that interact with each other more frequently than with other individuals in a population; groups or modules of highly connected individuals. High modularity networks have dense connections between nodes within modules but few connections (between nodes) in different modules (Baden et al., 2020;Godfrey et al., 2014).

Node
An object in a network, such as an individual (Croft et al., 2016;Godfrey et al., 2014).

Social preference
Selection of one element (e.g., individual) more frequently over another element (e.g., individual) in the context of a social environment. Non-random, repeated interactions with certain individuals that are the foundation of social relationships. Also termed preferred association (Bakeman, 1997;Croft et al., 2016;Godfrey et al., 2014;Krause et al., 2015).

NETWORK ANALYSIS DETAILS
In an interaction matrix, each node ( where n is the number of individuals in the network and d ij is the shortest distance between individuals i and j. CC i ranges from 0 to 1 with values closer to 1 indicating higher connectivity of an individual in relation to all others in the population (Loughran et al., 2015).

TA B L E A 8 (Continued)
F I G U R E A 1 Minimum convex polygons (MCP) showing home ranges for females CA-02 and CA-77 that alternated between communal dens (den ID: AD-1 and AD-5) and private winter shelters in different years. Note the consistency in CA-02's annual home range size and shape. See main text for additional details.